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6*sin(x/4-pi/12)-6=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
     /x   pi\        
6*sin|- - --| - 6 = 0
     \4   12/        
$$6 \sin{\left(\frac{x}{4} - \frac{\pi}{12} \right)} - 6 = 0$$
Solución detallada
Tenemos la ecuación
$$6 \sin{\left(\frac{x}{4} - \frac{\pi}{12} \right)} - 6 = 0$$
es la ecuación trigonométrica más simple
Transportemos -6 al miembro derecho de la ecuación

cambiando el signo de -6

Obtenemos:
$$6 \sin{\left(\frac{x}{4} - \frac{\pi}{12} \right)} = 6$$
Dividamos ambos miembros de la ecuación en -6

La ecuación se convierte en
$$\cos{\left(\frac{x}{4} + \frac{5 \pi}{12} \right)} = -1$$
Esta ecuación se reorganiza en
$$\frac{x}{4} + \frac{5 \pi}{12} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{x}{4} + \frac{5 \pi}{12} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
O
$$\frac{x}{4} + \frac{5 \pi}{12} = \pi n + \pi$$
$$\frac{x}{4} + \frac{5 \pi}{12} = \pi n$$
, donde n es cualquier número entero
Transportemos
$$\frac{5 \pi}{12}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$\frac{x}{4} = \pi n + \frac{7 \pi}{12}$$
$$\frac{x}{4} = \pi n - \frac{5 \pi}{12}$$
Dividamos ambos miembros de la ecuación obtenida en
$$\frac{1}{4}$$
obtenemos la respuesta:
$$x_{1} = 4 \pi n + \frac{7 \pi}{3}$$
$$x_{2} = 4 \pi n - \frac{5 \pi}{3}$$
Gráfica
Respuesta rápida [src]
     7*pi
x1 = ----
      3  
$$x_{1} = \frac{7 \pi}{3}$$
x1 = 7*pi/3
Suma y producto de raíces [src]
suma
7*pi
----
 3  
$$\frac{7 \pi}{3}$$
=
7*pi
----
 3  
$$\frac{7 \pi}{3}$$
producto
7*pi
----
 3  
$$\frac{7 \pi}{3}$$
=
7*pi
----
 3  
$$\frac{7 \pi}{3}$$
7*pi/3
Respuesta numérica [src]
x1 = -17.8023600559622
x2 = -68.0678391304132
x3 = 82.7286085015994
x4 = -17.8023574989498
x5 = 82.7286062922239
x6 = 7.33038150387412
x7 = 82.7286071852077
x8 = -42.9351008549945
x9 = -17.8023567520737
x10 = -93.2005841085706
x11 = 57.5958633811658
x12 = -68.0678398450346
x13 = 7.33038093273724
x14 = 57.5958638671306
x15 = 32.4631239639104
x16 = -42.9350990027676
x17 = 82.7286079882937
x18 = 132.994091564363
x19 = -17.8023563307113
x20 = 32.463124844372
x21 = 32.4631256206845
x22 = -17.8023608250547
x23 = -42.9350991093679
x24 = 32.4631223663587
x25 = -93.2005820590014
x26 = 107.861345925974
x27 = 57.5958664351449
x28 = -42.9351000077101
x29 = -68.0678390250001
x30 = 7.33038388254836
x31 = 57.5958673787099
x32 = -42.935097688124
x33 = 7.33038408158933
x34 = 7.33038256421289
x35 = 107.861349234482
x36 = -93.2005800960027
x37 = -93.2005823421457
x38 = 57.5958666500949
x39 = -17.8023604120996
x40 = 7.33038471187791
x41 = -93.2005800826288
x42 = 82.7286085168235
x43 = -42.9351004065219
x44 = 82.7286047530984
x45 = 7.33038086369274
x46 = -68.0678387701177
x47 = 32.4631225830263
x48 = -42.9351014702332
x49 = 7.33038490934731
x50 = -17.8023583238364
x51 = -17.8023592782964
x52 = 7.330383149795
x53 = -68.0678416225784
x54 = 57.5958671046355
x55 = -42.9351016316325
x56 = -93.2005838656637
x57 = -68.0678392167093
x58 = 82.7286044899893
x59 = 82.7286054191576
x60 = 57.5958646679633
x61 = 32.463125964147
x62 = -17.8023566054739
x63 = 82.7286052878168
x64 = -68.0678407671846
x65 = 32.4631230688373
x66 = 7.33038322619152
x67 = 32.4631260979099
x68 = -68.0678423888361
x69 = -68.0678428451497
x70 = 32.463122032436
x71 = -93.2005814473133
x72 = -42.9350975767139
x73 = -68.067842646263
x74 = -42.9350982758384
x75 = 7.33038232907484
x76 = 32.4631229528066
x77 = -93.2005832098587
x78 = 57.5958657457606
x79 = 82.7286063439891
x80 = 57.5958655582303
x81 = -93.2005806375113
x82 = -17.8023600141246
x83 = 57.5958633439357
x83 = 57.5958633439357